Interferometers for optical coherence domain reflectometry

ABSTRACT

An interferometer system includes an optical radiation source, an optical circulator connected between the optical radiation source and a sample location for transmitting optical radiation from the optical radiation source to the sample location, an output of the optical circulator connected to direct optical radiation to an optical detector. Various embodiments of such a system are possible. A method of performing OCDR or OCT imaging of a sample which involves the steps of: (a) producing low coherence optical radiation; (b) directing at least some of the low coherence optical radiation through an optical circulator to the sample; (c) reflecting at least some of the low coherence optical radiation off of the sample; and (d) detecting at least some of the reflected low coherence optical radiation and producing an electrical signal corresponding thereto.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.10/646,202, filed Aug. 22, 2003, now U.S. Pat. No. 7,102,756, which is adivisional of U.S. application Ser. No. 09/393,761, filed Sep. 10, 1999,now U.S. Pat. No. 6,657,727, which claims the benefit of U.S.Provisional Application No. 60/100,032, filed Sep. 11, 1998, the entiredisclosures of which are incorporated by reference.

FUNDING

This invention was made with government support under NSF Grant No.BES9624617. The government has certain rights in the invention.

BACKGROUND OF THE INVENTION

Optical Coherence Tomography (OCT) is a novel imaging technique whichallows for noninvasive cross-sectional imaging in scattering or cloudymedia with high spatial resolution and high dynamic range. OCT is atwo-dimensional extension of Optical Coherence-Domain Reflectometry(OCDR) which is also commonly referred to as Optical Low CoherenceReflectometry (OLCR), in which a low temporal coherence light source isemployed to obtain precise localization of reflections internal to aprobed structure along the optic axis. The one-dimensional rangingtechnique of OCDR/OLCR has previously been utilized for characterizationof bulk-, integrated-, and fiber-optic structures, as well as biologicaltissues. In OCT, this technique is extended to provide for scanning ofthe probe beam in a direction perpendicular to the optic axis, buildingup a two-dimensional data set comprising a cross-sectional image ofinternal tissue backscatter.

Ophthalmic Applications of OCT

OCT has previously been applied to imaging of biological tissues in vivoand in vitro, although the majority of initial biomedical imagingstudies concentrated on transparent structures such as the eye. Initialophthalmic imaging studies demonstrated significant potential for OCTimaging in routine examination of normal and abnormal ocular structures,including imaging of the cornea, iris, and other structures of theanterior eye; the lens and lens capsule; and numerous structures in theposterior eye, including the neurosensory retina, retinal nerve fiberlayer, retinal pigment epithelium, and choroid. In OCT examination ofthe retina, initial in vivo clinical studies have demonstrated itsutility in aiding diagnosis in a variety of vitreoretinal diseases,including macular hole, macular degeneration, detached retina, andglaucoma. Clinical trials of OCT imaging for ophthalmic applications arecurrently under way at several centers, and a commercial ophthalmic OCTscanner is available from Humphrey Systems of Dublin, Calif.

OCT Imaging in Highly Scattering Media

Several recent publications have demonstrated the potential applicationsof OCT in highly scattering media for the measurement of tissue opticalproperties and imaging. Optical imaging in scattering media such asbiological tissue is in general a very difficult problem, particularlyfor techniques such as OCT which depend primarily upon unscattered orsingly-scattered light for image formation. It has been observed inpreliminary studies and theoretical treatments that thissingly-scattered gating requirement practically limits OCT imaging to auseful penetration depth of a few millimeters at best in nontransparenthuman tissues. Nonetheless, several authors have identified diagnosticscenarios in which a technique for improved, non-invasive 10-20-micronscale optical imaging near tissue surfaces has significant potential forclinical utility. These include applications of OCT imaging in skin,teeth, vascular tissues, and gastrointestinal mucosa. The latter twoexamples are significant since with its fiber optic implementation, OCTis readily adaptable to minimally invasive diagnostic modalities such ascatheterization or endoscopy. OCT system implementations featuring thehigh-speed imaging acquisition necessary for in vivo application andcatheter/endoscopic delivery have been reported. The application of OCTto biomedical imaging provides the potential for sub-surface tissuecharacterization with sufficient resolution to provide microscopicmorphological information relevant to pathological diagnosis without theneed for biopsy.

OCT Imaging in Industrial Processing

Recent publications have also illustrated the potential applications ofOCT for imaging in cloudy or turbid non-biological media in industrialprocessing in the manufacturing industry. OCT imaging may be useful foron-line process control or product testing and evaluation. Initialexperiments have demonstrated OCT imaging in ceramic and other highlyscattering materials, as well as for the characterization of the surfacetopology of opaque industrial materials such as metals (i.e., ballbearings).

OCT Qualitative Technical Description

Optical coherence tomography performs micron-scale topographic imagingof internal tissue microstructure using a combination of the principlesof low-coherence interferometry and confocal microscopy. Reference ismade to FIG. 1 illustrating an exemplary OCT system 10 in which thetissue to be examined is placed in the sample arm 12 of a Michelsoninterferometer illuminated by a broadband light source 16. Due to thelimited coherence length of the source (typically 10-15 microns), lightreturning from the reference arm 18 and light backscattered by internalsample reflections interferes constructively or destructively only whenthe interferometer arm optical path lengths are matched to within thesource coherence length. Scanning the reference arm 18 length through aposition corresponding to the depth of a reflecting site within thesample generates a localized interference pattern, which is recorded asa localized modulation of the detector current as a function of thereference arm position. A beamsplitter 20, optical detector 22,transimpedance amplifier 24, demodulator 26, A/D converter 28, anddisplay 30 are also shown. The detector current generated by a samplecontaining multiple reflecting sites distributed along its depth (suchas biological tissue) contains the sum of multiple, overlapping copiesof this interference pattern. A map of tissue reflectivity versus depthor “A-Scan” is obtained by scanning the reference mirror 32 at constantvelocity, while recording the envelope of the detector current. Theenvelope may be recorded with high dynamic range by scanning thereference mirror 32 at fixed velocity, and demodulating the detectorcurrent at the resulting Doppler frequency. Cross-sectional images oftissue backscatter or “B-Scans” may be acquired by obtaining sequentialA-scans while scanning the probe beam across the tissue surface using alateral beam scanning mirror 33 or some other lateral scanning opticdevice. The resulting two-dimensional datasets are plotted as gray-scaleor false-color images.

A significant advantage of using low-coherence interferometry for signaldetection is that the interferometer 14 acts as an optical heterodynedetector, providing a dramatic expansion in dynamic range compared todirect detection of scattered light. Since the interferometric componentof the detector current is proportional to the product of the electricfield amplitudes returning from each arm, the detected envelope signalis proportional to the square root of the sample power reflectivity.Extremely faint reflections in the sample (˜10⁻¹¹ times the incidentoptical power) are routinely detected in A-scans recorded in a fractionof a second. As illustrated in FIG. 1, the interferometer 14 can also beimplemented using inexpensive semiconductor sources and detectors, andflexible single-mode optical fibers suitable for remote imaging throughminimally invasive diagnostic instruments.

Signal-To-Noise Ratio in OCDR and OCT

A significant limitation in the use of OCDR and OCT in highly scatteringmedia is that the OCT probe light is very strongly (exponentially)attenuated in the scattering material, thus limiting the imaging depthwhich can be achieved in a given amount of time for a given sensitivity.For a conventional OCT system in which a 50/50 beamsplitter 20 is usedin the Michelson interferometer, the signal to noise ratio (SNR) of thedetected electronic signal in the shot-noise limit is given by Eq. (1)below:

$\begin{matrix}{{SNR} = \frac{\rho\; P_{s}R_{s}}{2{qB}}} & (1)\end{matrix}$In this expression, SNR is signal-to-noise ratio (a measure of thesensitivity which also relates to imaging depth in scattering media), ρis the detector responsivity, P_(s) is the optical power incident on thesample, R_(s) is the optical power reflectivity of the sample, q is thecharge on the electron, and B is the detector bandwidth. The lattervariable B is inversely proportional to the time required to obtain anOCDR scan or OCT image. The shot-noise limit under which this expressionis calculated is well known to those practiced in the art to be the bestpossible performance (i.e., to give the best value for S/N) which can beachieved in an optical detection system. Even though not allimplementations of OCDR and OCT may actually achieve true shot-noiselimited performance and therefore may not be strictly governed by Eq.(1), most implementations aim to be near this limit and the equation isstill a useful guideline illustrating the trade-offs betweensensitivity, source power, and image acquisition time in this limitingcase of the best possible performance.

Equation (1) makes clear that there is a trade-off between sensitivityor depth, imaging time, and the source power incident on the sample inOCDR and OCT. Increases in imaging speed, for example, may only beachieved through either a decrease in S/N or an increase in powerincident on the sample. Increases in sensitivity or imaging depth (bothproportional to S/N) may only be obtained by increasing either theimaging time or the power on the sample. For industrial and medicalimaging applications, it is desirable to image as rapidly as possible,at a rate of at least several images per second. Recently, newtechnology has been developed permitting OCT image acquisition up tovideo rate (30 images/second), and high power low-coherence sources havebecome available to partially compensate for the decrease in sensitivitywhich necessarily accompanies any increase in imaging speed according toEq. (1). However, these high power sources are very expensive, and stillare not sufficiently powerful to allow for clinically acceptable qualityimaging at video rate (or even at the ˜10 images/second rate common toultrasound imaging).

Detector Power Limitations for Shot-Noise Limited Performance

Two requirements on the amount of optical power which may be incident onthe detector must be met in order to be at or near the shot-noise limitin OCDR and OCT. The first requirement is that the total optical powerincident on the detector 22 cannot be arbitrarily high in order for shotnoise to dominate over excess intensity noise for available sources. Forsystems with optical sources 16 which emit low power, this is not aproblem. However, recent developments in source technology have resultedin the availability of higher power sources (10-20 mW) which are veryattractive for high-speed imaging since the higher sample arm powerpartially compensates for the increased bandwidth B necessary for higherspeed imaging, according to Eq. (1). Since most industrial andbiological samples have very low reflectivity, they do not reflect anappreciable amount of sample arm light power onto the detector 22.However, in conventional systems employing such high power sources, anattenuator must be placed in the reference arm 18 in order to approachthe shot noise limit. This represents a waste of up to 50% of thevaluable and expensive source power, which is lost in an attenuator. Itwould be much better if this power could instead be directed onto thesample, so it could contribute to imaging performance as describe in Eq.(1). Clearly there is a need for an improved interferometer design forOCDR and OCT which avoids power losses due to attenuation required toachieve shot-noise-limited performance on the detector.

The second requirement on the amount of power on the detector is that itmust be sufficiently high so that shot noise dominates over thermalnoise in the detector. For most commonly available semiconductordetectors in the visible and near-infrared regions of the spectrum, thepower on the detector must be at least approximately 1 μW for a typicallow speed system using a detector with a bandwidth less thanapproximately 100 kHz, to 10 μW for a typical high speed system using adetector with a bandwidth of approximately 10 MHz. Thus, there is arange of acceptable power levels which will achieve shot-noise limitedperformance at the detector, and under the assumption that most of thelight reaching the detector comes from the reference arm (i.e., underthe approximation of a weakly reflecting sample), this places alimitation on the range of acceptable power levels in the reference arm,which is typically in the range of between 1 μW and 10 μW.

Reciprocal Optical Elements: The Beam splitter/Fiber Coupler

In conventional OCDR and OCT, the central element of the Michelsoninterferometer is a standard beamsplitter 20 which transmits or splitssome fraction of the power (typically 50%) of the incident light powerinto each of the sample and reference arms 12 and 18. In a bulk opticinterferometer the beamsplitter 20 may be a mirror with a partiallyreflective coating, while in a fiber optic interferometer thebeamsplitter is composed of a pair of fibers partially fused togetherwhich is known as a fiber coupler. As illustrated in FIG. 2, thebeamsplitter may be abstracted as a four-port optical element with twoinputs (labeled as I1 and I2), and two outputs (labeled as O1 and O2).The abstracted beamsplitter illustrated in FIG. 2 is characterized by asplitting ratio α, such that a fraction α of the light power incident atport I1 (neglecting small internal losses of the beamsplitter) istransmitted to port O2, while the fraction (1−α) of the light powerincident at port I1 is transmitted to port O1. A similar statementapplies to light power incident at port I2: in this case, a fraction αof the light power incident at port I2 (neglecting small internal lossesof the beamsplitter) is transmitted to port O1, while the fraction (1−α)of the light power incident at port I1 is transmitted to port O2. Thisconventional beamsplitter is known as a reciprocal optic element becauselight which is input into either of the output ports O1 or O2 willreciprocally be transmitted to the input ports I1 and I2. Specifically,a fraction α of any light power incident at port O1 is transmitted toport I2, while the fraction (1−α) of the light power incident at port O1is transmitted to port I1. Finally, a fraction α of any light powerincident at port O2 is transmitted to port I1, while the fraction (1−α)of the light power incident at port O2 is transmitted to port I2.

Reciprocal Power Losses in Conventional OCDR and OCT

A second clear drawback of the use of the conventional Michelsoninterferometer topology in OCDR and OCT is that significant reflectedsample arm power is lost because it is inevitably directed back into thesource, rather than being collected by the detector 22. In thetheoretical analysis which leads to Eq. (1) (derived in the limit of alow reflectivity sample) the noise power is proportional to the amountof power incident on the detector 22 from the reference arm 18, whilethe signal power is proportional to the product of the coupler splittingratios from the source 16 to the sample arm 12 and from the sample arm12 to the detector 22. In the 50/50 (α=0.5) Michelson interferometerused in conventional OCT (see FIG. 1), the light from the broadbandsource 16 is split evenly between the sample and reference arms, whilelight returning from both the sample and reference arms is split againinto the input arms 34 and 36 containing the source 16 and detector 22.Thus, the detected signal power is proportional to the product of the50% splitting ratio from the source 16 to the sample arm 12, and the 50%splitting ratio from the sample arm 12 to the detector 22, for acombined sample power double splitting ratio of 25%. Fiber couplers withcoupling ratios other than 50% are commonly available; however, theiruse in the Michelson configuration is even worse. For example, if a90/10 beamsplitter directs 90% of the source light into the sample armand only 10% of the light into the reference arm, then the combinedsample power splitting ratio is only 9% (10% of the 90% of the sourcelight power incident on the sample).

The modified form of Eq. (1) which is correct for the case of arbitrarysplitting ratio is set forth as Eq. (2):

$\begin{matrix}{{SNR} = \frac{\rho\; P_{O}R_{s}{\alpha\left( {1 - \alpha} \right)}}{qB}} & (2)\end{matrix}$Here, α is the coupler splitting ratio and P_(o) is the source power.Eq. (2) is consistent with Eq. (1) since in the case of Eq. (1),P_(s)=P_(o)/2. Clearly, the SNR in Eq. (2) is optimized for α=0.5, or a50% coupling ratio.Motivation for the Invention

Until the development of the present invention, the only method toincrease the sensitivity or acquisition rate in OCDR and OCT was toincrease the source power. Increases in the source power are veryexpensive given current source technology. The design of conventionalOCDR and OCT interferometers with reciprocal beamsplitters, is veryinefficient with the expensive source power, since up to 50% of thesource power is lost due to attenuation of the reference arm, and anadditional 50% of the power reflected from the sample is wasted by beingdirected back into the source. An interferometer design which avoidsboth of these problems could be up to a factor approaching 4 moreefficient, and could thus obtain better quality images at the highspeeds required for commercial applications of OCDR and OCT technology.Thus, there is a clear need for an invention which makes more efficientuse of broadband source light than the conventional OCT interferometer.

SUMMARY OF THE INVENTION

In one aspect of the invention an interferometer system includes anoptical radiation source, an optical circulator connected between theoptical radiation source and a sample location for transmitting opticalradiation from the optical radiation source to the sample location, andan output of the optical circulator is connected to direct opticalradiation to an optical detector. Various embodiments of such a systemare provided.

For example, three embodiments are provided in which an interferometerincludes a low coherence optical radiation source and a firstbeamsplitter having a first input connected to receive optical radiationfrom the low coherence optical radiation source. A first nonreciprocaloptical element (such as an optical circulator) has a first inputconnected to receive optical radiation from a first output of the firstbeamsplitter, a first output for directing optical radiation from thefirst input to a sample to be imaged, a second input connected in commonwith the first input for receiving optical radiation reflected by thesample, and a second output for receiving optical radiation from thesecond input. A second beamsplitter has a first input connected toreceive optical radiation from the second output of the nonreciprocaloptical element, and an optical radiation detector is connected toreceive optical radiation from the second beamsplitter.

Two embodiments are provided in which an interferometer include a lowcoherence optical radiation source and a nonreciprocal optical element(such as an optical circulator) having a first input connected toreceive optical radiation from the low coherence optical radiationsource and a combination first output/second input. A beamsplitter isprovided with a first input connected to the combination firstoutput/second input of the nonreciprocal optical element, a first outputconnected for directing optical radiation to a sample to be imaged andfor receiving reflected optical radiation from the sample to be imaged,and a second output connected for directing optical radiation to areference delay element and for receiving reflected optical radiationfrom the reference delay element.

Another aspect of the invention also provides a method of performingOCDR or OCT imaging of a sample which involves the steps of: (a)producing low coherence optical radiation; (b) directing at least someof the low coherence optical radiation through an optical circulator tothe sample; (c) reflecting at least some of the low coherence opticalradiation off of the sample; and (d) detecting at least some of thereflected low coherence optical radiation and producing an electricalsignal corresponding thereto.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of a traditional OCT system;

FIG. 2 is a schematic illustration of a reciprocal beamsplitter;

FIG. 3 is a schematic illustration of an optical circulator;

FIG. 4 is a schematic illustration of an optical circulator implementedusing a polarizing beamsplitter and a Faraday rotator;

FIG. 5 is a schematic illustration of a Mach-Zehnder interferometerconfiguration;

FIG. 6 is a schematic illustration of one interferometer embodimentaccording to the invention;

FIG. 7 is a schematic illustration of another interferometer embodimentaccording to the invention;

FIG. 8 is a schematic illustration of another interferometer embodimentaccording to the invention;

FIG. 9 is a schematic illustration of another interferometer embodimentaccording to the invention; and

FIG. 10 is a schematic illustration of another interferometer embodimentaccording to the invention.

FIG. 11 is a schematic illustration of another interferometer embodimentaccording to the invention;

FIG. 12 is a schematic illustration of another interferometer embodimentaccording to the invention; and

FIG. 13 is a schematic illustration of another interferometer embodimentaccording to the invention.

DETAILED DESCRIPTION

The invention, which is described in several embodiments, consists ofnovel interferometer designs for OCDR and OCT which employnon-reciprocal optical elements in order to make more efficient use ofthe source light power.

The critical technology which enables the present invention arenonreciprocal optical elements which have recently become commerciallyavailable, such as the optical circulator (OC) and Faraday Rotator (FR).An optical circulator 50, as illustrated in FIG. 3, is a threeportoptical device in which all power incident on input port I1 (except forsmall internal losses) is directed into output port O1, which is commonwith the second input port I2. All light incident on the input port I2(except for small internal losses) is similarly directed into the outputport O2. Polarization-independent optical circulators are commerciallyavailable, in which the performance is independent of the polarizationstate of the light at the input or output ports. Bulk-optic andfiber-optic versions are commercially available; fiber-optic versionsare particularly suitable for use in fiber-optic implementations of OCDRand OCT. An example of a commercially available fiberoptic opticalcirculator which would be suitable for use in the designs disclosed inthis application is Model #60-13-3 from Princeton Optics, Inc., ofEwing, N.J.

A second nonreciprocal optical element suitable for use in improving theperformance of OCDR and OCT is the Faraday rotator. A Faraday rotator isa device which rotates the polarization state of a light beam whichtraverses it, by an angle which is a characteristic (fixed or variable)property of the rotator. In particular, a polarization-dependent form ofoptical circulator 52 may be constructed from a 45° Faraday rotator 54and a polarizing beamsplitter (PBS) 56, as illustrated in FIG. 4. Apolarizing beamsplitter 56 is an optical device which either transmitsor reflects light incident upon it depending upon the polarization stateof the incident-light. As illustrated in FIG. 4, vertically polarizedlight incident on a PBS 56 oriented as illustrated will pass through thePBS 56 and be incident on the FR 54. The rotation state of the lightwill be rotated by 45° by the FR 54, and may then be directed onto areflective element or sample 58, which must preserve the polarizationstate of the light reflected. The reflected light will be rotatedanother 45° by the FR 54, and will then be reflected by the PBS 56 sinceits polarization state has been rotated by a total of 90° from that ofthe incident light. This configuration is effectively a form of opticalcirculator 52, in which the incident light is considered as enteringport I1, the transmitted and reflected light transit ports O1 and I2,respectively, and the output light exits port O2. It should be notedthat the device illustrated in FIG. 4 is just one possibleimplementation of an optical circulator, and this is not an optimalimplementation in many cases because the polarization state of the lightentering port I2 must match the polarization state of the light exitingport O1, thus the sample must preserve polarization. Optical circulatorsare commercially available which allow for arbitrary polarization statesat any of the input ports I1 or I2. Thus, in the remainder of thistechnical description reference will be made only to optical circulatorsin general, and not specifically the PBS/FR implementation. However, itshould be understood that this implementation may be used whenever thesample does in fact preserve the polarization state of the lightreflected from it, and this implementation may in fact be less expensivethan the alternative in that case. An example of a polarizingbeamsplitter and a Faraday rotator suitable for use in the designsdisclosed in this application are Model #10FC16 from NewportCorporation, Irvine, Calif., and Model #MOFI6CW100000 from E-TekDynamics, San Jose, Calif., respectively.

A second enabling technology for the improved efficiency OCDR/OCTdesigns disclosed in this application is the use of dual-balanced(differential) detection of optically heterodyned signals. Dual-balanceddetection is useful when two optical signals with approximately equal DCpower, but with AC components which are 180° out of phase, are bothpresent. This is the case, for example, in previously publishedtransmissive implementations of OCDR and OCT which employ a Mach-Zehnderinterferometer configuration 60 as illustrated in FIG. 5. Thelow-coherence source light 62 is incident on the first beamsplitter 64,which splits the light evenly between sample 66 and reference 68 arms.The reference arm 68 includes a variable optical delay 70, while thesample arm 66 includes an optical element or sample 72, which isilluminated in transmission. Light from the sample and reference arms isrecombined in the second beamsplitter 74, and the resulting mixed lightis split evenly between two detectors D1 and D2 whose responsivity iscarefully matched. These detectors D1 and D2 are placed in an electroniccircuit 76 whose output 78 is equal to the amplified difference betweenthe photocurrents produced by the two detectors. This detection schemehas two advantages. First, since the light intensity incident on eachdetector surface as a function of reference arm delay is 180° out ofphase, the envelope of difference signal between the two detectorcurrents (as the reference delay is scanned) is equal to twice theamplitude of the AC component of the photocurrent of each detector.Secondly, since any excess noise present in the light propagatingthrough the interferometer will be common to both detectors, this excessnoise will be eliminated by the difference operation. This detectionscheme depends upon careful matching of the DC component of the lightpower incident on each detector as well as the careful matching of theresponsivities of both detectors to be effective, althoughself-balancing detectors which include self-adjusting variable gains forthe two detectors are commercially available. An example of a highsensitivity auto-balancing photodetector suitable for use at lowfrequencies in the designs disclosed in this application is Model #2007from New Focus Corporation, of Santa Clara, Calif., and a balancedreceiver suitable for high-frequency applications is Model #1607, fromthe same vendor.

The final technology which is different from most previousimplementations for OCDR and OCT which is desirable for the novelhigh-efficiency embodiments is single-mode fiber optic couplers orbeamsplitters with splitting ratios other than 50/50. In thisapplication, we will denote such “unbalanced” couplers as having asplitting ratio of α, indicating that the fraction α of the light powerincident on port I1 is transmitted to port O2, while the fraction (1−α)of the light power incident on port I1 is transmitted to port O1, and soon. Using this notation, the standard 50/50 beamsplitter has α=0.5. Suchunbalanced beamsplitters are very commonly commercially available in thefiber optic marketplace. An example of a singlemode fiber coupler with asplitting ratio of 90/10 which is suitable for use in the designsdisclosed in this application is Model #28 CBB 102/001/AS from MellesGriot Corporation, Irvine, Calif. Other couplers with arbitrarysplitting ratios are available from this and other vendors.

Novel OCDR/OCT Interferometer Designs

We disclose five novel interferometer configurations whichsimultaneously avoid the losses associated with reference armattenuation and with reciprocal power losses in conventional OCDR/OCT.These configurations are illustrated in FIGS. 6-10. Most of theseconfigurations involve unbalanced splitters. In this disclosure, wefirst describe the design qualitatively. Then, for each embodiment,design equations are provided for optimizing the splitting ratios inorder to obtain maximum signal to noise for a given source power andminimum power required by the detector for shot noise-limitedperformance. Finally, for each embodiment, typical values are presentedassuming typical values in the design equations. In each interferometerconfiguration the various optical elements could typically beinterconnected using fiber optic technology, but it is recognized thatother technologies such as integrated-optic or conventional bulk-optic(i.e. discrete optical elements) could also be used for interconnectionof the optical elements.

Embodiment #1

The embodiment illustrated in FIG. 6 uses an interferometerconfiguration 100 similar to the Mach-Zehnder illustrated in FIG. 5,except that both couplers or beamsplitters 102 and 104 may beunbalanced. In FIG. 6, an unbalanced singlemode coupler 102 splits lightfrom the source 106 and sends most of the source light power to thesample arm 108 of the interferometer 100. The splitting ratio of theunbalanced coupler 102 is selected such that the amount of powerdirected into the reference arm 110 is within the suitable range forshot-noise limited detection. An optical circulator 112 directs thesample arm light onto the sample 114, and directs light returning fromthe sample into a second singlemode coupler 104, which in general mayalso be unbalanced. In the reference arm 110, a second opticalcirculator 116 directs reference arm light onto a variable referencedelay element 118, and directs light returning from the delay 118 intothe other input port of second single mode coupler 104. Thisconfiguration places most of the source light on the sample 114, thusautomatically eliminating the power loss in the conventionalinterferometer due to purposeful attenuation of reference arm light toachieve shot-noise limited detection. Secondly, this configurationdirects all of the light returning from the sample 114 to a detector120, thus none of the reflected sample arm light is lost to reciprocallosses as in the conventional design. The intensities incident on thedetectors D1 and D2 as a function of reference arm delay are out ofphase, so differential detection may be achieved simultaneous withcommon-mode rejection of excess intensity noise.

If the splitting ratio of the second splitter 104 is chosen to be 50/50(i.e., α₂=0.5), then equal powers are incident on each of the dualdetectors D1 and D2, and true dual-balanced detection may be achieved.In this case, the expression for the signal-to-noise ratio is given asEq. (3):

$\begin{matrix}{{SNR} = \frac{\rho\;{P_{0}\left( {1 - \alpha_{1}} \right)}T_{c}^{2}R_{s}}{qB}} & (3)\end{matrix}$where ρ is the detector responsivity, P₀ is the optical source power, α₁is the splitting ratio of the first singlemode coupler 102, T_(c) is thetransmission through-the circulator, R_(s) is the reflectivity of thesample, q is the electronic charge, and B is the bandwidth of thedetection electronics. We also disclose an expression for the optimalsplitting ratio for the first coupler 102, which ensures that there issufficient reference arm power to allow for shot-noise limiteddetection, but at the same time places the maximum possible power on thesample. This expression is given as Eq. (4):

$\begin{matrix}{\alpha_{1} = \frac{2P_{\min}}{P_{0}T_{c}^{2}R_{r}}} & (4)\end{matrix}$where R_(r) is the reflectivity of the reference arm delay line. Here,P_(min) is the minimum power which must be present at the detector 120in order to ensure shot noise dominates receiver noise. Assuming thetypical value of P_(min)=10 μW, the values of P₀=10 mW, T_(c)=0.85, andR_(r)=0.9, we obtain an optimal splitting ratio for the first coupler ofα₁=0.0031. Using a coupler with this splitting ratio as the firstcoupler 102 in FIG. 6, and a coupler with the value of α₂=0.5 as thesecond coupler 104 provides a signal-to-noise ratio advantage of afactor of 2.88 (or 4.60 dB) over the conventional Michelson OCDR/OCTarrangement. Thus, using this optimal embodiment, OCT images could beobtained at the same rate with a factor of 2.88 times bettersensitivity, or alternatively at an acquisition rate of 2.88 timesfaster with the same sensitivity as in conventional OCT. The use ofembodiment #1 with α₂=0.5 allows for the maximum possible gain indynamic range as compared to the conventional design, and will be thepreferred embodiment of all of those disclosed when absolutely thehighest dynamic range performance must be achieved regardless of theadded expense of two optical circulators 112 and 116.

The splitting ratio of the second splitter 104 in embodiment #1 may ingeneral be chosen to be any value, however a convenient choice may be tochoose a high splitting ratio, for example α₂=α₁, and then to use onlythe top detector D1 for signal detection. This alternative form ofembodiment #1 eliminates the expense of the second matched detector D2and the associated differential gain electronics. In this case, theexpression for the signal-to-noise ratio is given as Eq. (5):

$\begin{matrix}{{SNR} = \frac{\rho\;{P_{0}\left( {1 - \alpha_{1}} \right)}\left( {1 - \alpha_{2}} \right)T_{c}^{2}R_{s}}{qB}} & (5)\end{matrix}$where α₁=α₂ is the splitting ratio of both couplers 102 and 104, andP_(i) is the source power. In this case of α₂=α₁ the expression for theoptimal value of α₁ is given as Eq. (6):

$\begin{matrix}{\alpha_{1} = {\alpha_{2} = \sqrt{\frac{P_{\min}}{P_{0}T_{c}^{2}R_{r}}}}} & (6)\end{matrix}$Under the same assumptions that P_(min)=10 μW, P₀=10 mW, T_(c=)0.85, andR_(r)=0.9 as stated above, the optimal value of both couplers is thenα₂=α₁=0.039, and the corresponding signal to noise ratio advantage overconventional OCDR/OCT is a factor of 2.67 (or 4.26 dB).Embodiment #2

The interferometer 130 illustrated in FIG. 7 is similar to thatillustrated in FIG. 6, except that the expense of one of the opticalcirculators is avoided by use of a transmissive delay element 132 ratherthan a reflective reference arm delay. The transmissive delay element132 could be similar to element 70 illustrated in FIG. 5. All otheradvantages of the first embodiment are preserved. The expression for thesignal-to-noise ratio in the case of α₂=0.5 (dual-balanced detection) isthe same as equation (3), in which case the expression for the optimalfirst coupler splitting ratio is:

$\begin{matrix}{\alpha_{1} = \frac{2P_{\min}}{P_{0}R_{r}}} & (7)\end{matrix}$Under the assumptions that P_(min)=10 μW, P₀=10 mW, T_(c)=0.85, andR_(r)=0.9, the optimal value of the first coupler is then α₁=0.0022, andthe corresponding signal-to-noise ratio advantage over conventionalOCDR/OCT is a factor of 2.88 (or 4.59 dB), which is identical to thedual-detector version of embodiment #1. The expression for thesignal-to-noise ratio in the case of α₂=α₁ (one detector only) is thesame as equation (5); in this case the expression for the optimalcoupler splitting ratio is:

$\begin{matrix}{\alpha_{1} = {\alpha_{2} = \sqrt{\frac{P_{\min}}{P_{0}R_{r}}}}} & (8)\end{matrix}$In equations (7) and (8), the term R_(r) represents reference delay linetransmission, rather than reflectivity, since a transmissive delay lineis used rather than a reflective one. Under the assumptions thatP_(min)=10 μW, P₀=10 mW, T_(c)=0.85, and R_(r)=0.9, the optimal value ofboth couplers is then α₂=α₁=0.033, and the corresponding signal-to-noiseratio advantage over conventional OCDR/OCT is a factor of 2.70 (or 4.31dB), which is nearly identical to the single-detector version ofembodiment #1. The performance advantages for both versions of thisembodiment over conventional OCDR/OCT are the same as for interferometer100. Interferometer 130 will be the preferred embodiment whenimplementation of a transmissive delay line is practical, such as inrecently published high-speed OCT systems which use a novel referencedelay based on Fourier transform pulse shaping techniques, which arereadily amenable to implementation in a transmissive geometry.Embodiment #3

The interferometer 140 illustrated in FIG. 8 is also similar to thefirst embodiment of FIG. 6, except that interferometer 140 avoids theadditional expense of one optical circulator while still using areflective reference delay 118. This embodiment preserves all of theadvantages of the first embodiment, except that the gain in dynamicrange as compared to the conventional system is slightly less, becausethe optimal value of the first coupler 102 splitting ratio is somewhatsmaller than in embodiment #1 in order to compensate for the smallamount of reference arm power which is returned to the source 106 ratherthan placed on a detector. Interferometer 140 will be the preferred onewhen a slight loss in efficiency is worth the savings of the cost of oneoptical circulator.

If the splitting ratio of the second beamsplitter 104 in interferometer140 is chosen to be 50/50 (i.e., α₂=0.5), then equal powers are incidenton each of the dual detectors D1 and D2, and true dual-balanceddetection may be achieved. In this case, the expression for thesignal-to-noise ratio is the same as Eq. (3). The expression for theoptimal splitting ratio for the first coupler 102, which ensures thatthere is sufficient reference arm power to allow for shot-noise limiteddetection, but at the same time places the maximum power on the sample114, under the assumption that α₁ is small, is the same as given inequation (7). Thus, the typical value of rhte optimum splitting ratio α₁and the performance advantage of this embodiment over the conventionalMichelson arrangement (under the assumption that α₁ is small) areexactly the same s for the dual-detector version of embodiment #2. Theuse of interferometer 140 with α₂=0.5 allows for the second-highestpossible gain of all reflective delay embodiments disclosed in dynamicrange as compared to the conventional design, and will be the preferredembodiment when a reflective delay element must be used and the expenseof a second optical circulator as required in interferometer 100 of FIG.6 must be avoided.

The splitting ratio of the second splitter 104 in interferometer 140 mayin general be chosen to be any value, however a convenient choice may beto choose a high splitting ratio, for example α₂=α₁ and then to use onlythe top detector D1 for signal detection. This alternative form ofinterferometer 140 eliminates the expense of the second matched detectorD2 and the associated differential gain electronics. In this case, theexpression for the signal-to-noise ratio is the same as Eq. (5). In thiscase of α₂=α₁, under the assumption that both α₁ and α₂ are small, theoptimal values for α₂ and α₁ are the same as given in equation (8).Thus, the typical value for the optimum splitting ratios α₂ and α₁ andthe performance advantage of this embodiment over the conventionalMichelson arrangement (under the assumption that both α₂ and α₁ aresmall) are exactly the same as the single-detector version of embodiment#2.

Embodiment #4

The interferometer 150 illustrated in FIG. 9 is similar to theconventional Michelson interferometer arrangement, except that anoptical circulator 152 is placed between the low-coherence source 106and the fiber coupler or beamsplitter 154 and the beamsplitter 154 isunbalanced. The splitting ratio of the unbalanced coupler 154 isselected such that the amount of power directed into the reference arm156 is small enough to allow for shot-noise limited detection, but largeenough to avoid thermal detector noise. The optical circulator 152directs most of the light reflected from the sample 114 but only a smallfraction of the light returning from the reflective reference delayelement 118 onto the detector 156. Only a single detector 156 is neededin this configuration. This interferometer configuration places most ofthe source light on the sample 114, thus automatically eliminating thepower loss in the conventional interferometer due to purposefulattenuation of reference arm light to achieve shot-noise limiteddetection. Secondly, most of the light returning from the sample isdirected to the detector 156, thus only a small fraction of thereflected sample arm light is lost to reciprocal losses as in theconventional design.

The expressions and typical values for the signal-to-noise ratio and forthe optimal coupler splitting ratios for interferometer 150 are givenabove as Eqs. (5) and (6), respectively. The performance advantages forthis embodiment over conventional OCDR/OCT are the same as for thesecond implementation (with α₂=α₁,) of embodiment #1 of FIG. 6, i.e. asignal-to-noise advantage of 2.67 (4.26 dB) as compared to conventionalOCDR/OCT. Interferometer 150 is a preferred embodiment to the α₂=α₁,versions of embodiments #1 and #2, since it achieves the sameperformance with fewer components, i.e. with only one unbalanced couplerand one optical circulator.

Embodiment #5

The interferometer 160 illustrated in FIG. 10 is similar to thatillustrated in FIG. 9, except that a balanced coupler 162 is used inplace of the unbalanced coupler 154 in FIG. 9, and a dual-balanceddetector arrangement 164 is also used. This interferometer configurationdoes riot have the advantage of placing most of the source light on thesample, thus it will not be the preferred embodiment when the sourcepower is sufficient to preclude shot-noise limited detection. However,this interferometer configuration avoids both sample and reference armreciprocal losses by placing all of the light reflected from the sampleand reference arms 158 and 156 on a detector 164, and achieves a gain indynamic range of a factor of approximately 1.45 (1.60 dB) as compared tothe conventional arrangement. This will be the preferred embodiment whena low-power source is used and the expense of an unbalanced coupler mustbe avoided.

General Expression for Optimization of Coupler Splitting Ratios

We disclose a general procedure for optimizing the choice of couplersplitting ratios for those embodiments employing two beamsplittingcouplers. This procedure seeks to balance the requirements to place thelargest possible fraction of the source power on the sample, while atthe same time ensuring that there is sufficient power in the referencearm to ensure shot-noise limited detection for weakly reflectivesamples. For embodiments #1 and #2, this expression is given by equation(9):

$\begin{matrix}{{\alpha_{1}\alpha_{2}} = {\frac{P_{\min}}{P_{0}T_{c}^{2}R_{r}}.}} & (9)\end{matrix}$For embodiment #2, there is no reference arum circulator, so expression(9) applies if T_(c), is taken to be 1, and R_(r) is taken to meanreference delay line transmission, rather than reflectivity. Accordingto Eq. (9) there are an infinite number of possible choices for α₁, andα₂, however the choices α₂=0.5 (i.e., a 50/50 splitting ratio for thesecond coupler) and α₁=α₂ (i.e., the same splitting ratio for bothcouplers) are particularly useful. For embodiment #3, the expressionwhich optimizes the choice of splitting ratios is given by Eq. (10):

$\begin{matrix}{{{\alpha_{1}\left( {1 - \alpha_{1}} \right)}\alpha_{2}} = \frac{P_{\min}}{P_{0}R_{r}}} & (10)\end{matrix}$

As seen from the above embodiments, the primary commonality between theinterferometer configurations is the use of at least one nonreciprocaloptical element (preferably an optical circulator) which results inincreased efficiency. However, although generally undesirable it isrecognized that interferometer configurations in accordance with thepresent invention could be constructed with a relatively low efficiency(an efficiency similar to that of traditional systems).

Each of the various embodiments described provides an interferometersystem including an optical radiation source, a first optical circulatorand an optical detector. A first optical path extends from the opticalradiation source, through a first portion of the first opticalcirculator to a sample location, and from the sample location through asecond portion of the optical circulator to the optical detector.

In the embodiments of FIGS. 6-8, the interferometer system also includesa first beamsplitter positioned between the optical radiation source andthe optical circulator along the first optical path, and a secondbeamsplitter positioned between the optical circulator and the opticaldetector along the first optical path. In the embodiment of FIG. 9, theinterferometer system includes a second optical path extending from theoptical radiation source, through the first portion of the opticalcirculator to a reference location, from the reference location throughthe second portion of the optical circulator to the optical detector. Inthe embodiment of FIG. 10 the optical detector comprises first andsecond optical detectors, the first optical detector positioned at theend of the first optical path, and the interferometer further includes asecond optical path extending from the optical radiation source, throughthe first portion of the optical circulator to a reference location,from the reference location to the second optical detector.

The forgoing optimization equations were derived assuming shot noiselimited detection. This analysis is not adequate in situations wherethere is appreciable backreflection from the sample arm optics or whenthe optical source intensity noise exceeds the excess photon noisepredicted by the photon arrival statistics given the source bandwidth.In these cases, the following SNR analysis, which is more complete,should be used to optimize the splitting ratio. Note that some notationused hereafter differs from that used in the previous analysis.

In a dispersionless OCT system, the photocurrent at a detector will ingeneral be given by I_(d)=ρ(P_(r)+P_(s)+P_(x)+2√{square root over(P_(r)P_(s))}cos(k₀Δl)), where ρ is the detector responsivity. P_(r) isthe optical power incident on the photodetector reflected from thereference arm of the interferometer, P_(s) is that portion of theoptical power incident on the photodetector having been backscatteredfrom the sample that is coherent with the reference light, and P_(x) isthe optical power incident on the photodetector reflected from thesample arm of the interferometer which is incoherent with the referencelight. Also, k₀ is the center wavenumber of the optical source, and Δlis the optical path difference between the reference and sample arms.The signal photocurrent, I_(s), is the a.c., or interference term ofI_(d):I_(s)=2ρ√{square root over (P_(r)P_(s))}cos(k₀Δl)  (11)We express noise sources in terms of the photocurrent valiance σ₁ ². Thenoise sources to be included in this analysis are receiver noise σ_(re)², shot noise σ_(sh) ², and excess intensity noise σ_(ex) ². Receivernoise may be modeled as thermal noise in a resistance-limited receiverwith an effective load resistance R_(eff). Thermal noise is the randomthermal motion of electrons in a conductor, and the photocurrentvariance due to thermal noise is given by: σ_(re) ²=4k_(B)TB/R_(eff),where k_(B) is Boltzman's constant, T is temperature and B is thedetection bandwidth. For a commercial photoreceiver module, thephotocurrent variance due to receiver noise can be calculated directlyfrom the manufacturer specifications. For example, the manufacturer mayspecify input noise current (noise equivalent photocurrent density, e.g.2 pA/√{square root over (Hz)}), from which we calculate: σ_(re) ²=(2ρA/√{square root over (Hz)})²B . The random arrival of photons from amonochromatic light source is a Poisson process. The resultingphotocurrent variance is shot noise and is given by σ_(sh) ²=2qI_(dc)B,where q is the electronic charge and I_(dc) is the mean detectorphotocurrent. The random arrival of photons from a broadband, incoherentlight source is a Bose-Einstein process. The resulting photocurrentvariance has two terms: shot noise, and excess photon noise. Excessphoton noise is given by σ_(exp) ²=(1+V²)I_(dc) ²B/Δν, where V is thedegree of polarization of the source, and Δν is the effective linewidthof the source. Assuming a Gaussian power spectral density, Δν=√{squareroot over (π/2 ln(2))}cΔλ_(FWHM)/λ₀ ², where c is the speed of light,Δλ_(FWHM) is the full-width half-maximum wavelength bandwidth of thesource, and λ₀ is the center wavelength. This expression for excessphoton noise represents the minimum expected intensity noise for asource with a given effective linewidth. Some broadband optical sources,such as mode-locked femtosecond lasers, exhibit more than this minimumintensity noise. In order to generalize, we will write anotherexpression for excess intensity noise (or relative intensity noise):σ_(ex) ²=(RIN)I_(dc) ²B. Here, RIN (relative intensity noise) may bespecified by the manufacturer of the source, or it may be measured, orit may be calculated as RIN=(1+V² )Δν, which should be valid for thebroadband, incoherent sources typically used in OCT and OCDR. If RIN iscalculated using the expression above, then σ_(ex) ² is identical toσ_(exp) ².Assuming that the light intensity backscattered from the sample isnegligible compared to the reference power, the average, or d.c.photocurrent is given by I_(dc)≡(I_(d))=ρ(P_(r)+P_(x)), where thebrackets indicate the mean value. Thus, for the case of a singledetector, the total photocurrent variance is given by:σ_(i) ²=σ_(re) ²+σ_(sh) ²+σ_(ex) ².  (12)If balanced heterodyne detection is used, then excess intensity noise islargely cancelled. Taking into account extra retroreflected power fromthe sample arm, P_(x), however, a component of the excess photon noiseremains which is called beat noise and is given by σ_(bε)²=2(1+V²)I_(r)I_(x)B/Δν, where I_(r)=ρP_(r) and I_(x)=ρP_(x). Noise ineach of the detectors comprising the balanced receiver is independent,so their variances add and the total photocurrent variance in the caseof balanced heterodyne detection becomes:σ_(i) ²=2(σ_(re) ²+σ_(sh) ²+σ_(be) ²).  (13)It is important to note that all photocurrent variances have beenwritten in terms of one-sided noise spectral density functions (i.e.integrated over positive frequencies only), and that howeverdemodulation is performed, B is the width of the detection band-passfilter, as opposed to, for example, the cutoff frequency of ademodulation low-pass filter.

Other noise sources that are generated in an OCT system include flicker(1/f) noise, dark current noise, and quantization noise. Flicker noiseis avoided simply by ensuring a high enough signal carrier (heterodyne)frequency such that the signal bandwidth is well above dc (several kHzis sufficient). Dark current noise is the shot noise arising from thedetector dark current. It is generally small, and because it isindependent of incident light intensity, it is suppressed by theidentical method as suppressing receiver noise, that is, allowingsufficient light on the detector such that shot noise dominates.Quantization noise arises from an insufficient number of A/D bitssampling the signal. This can be avoided by selecting an A/D converterwith a sufficient dynamic range (the noise floor should be less than ½of the least significant bit), and by conditioning the signal such thatit fills the A/D dynamic range. Because these noise sources can besuppressed or avoided, they are not included in this SNR model.

We define SNR=<I_(s) ²>/σ_(i) ². From equation (11) above, themean-square signal photocurrent in a single detector can be written as:<I_(s) ²>=2ρ²P_(r)P_(s).  (14)For a balanced receiver, the total signal photocurrent is the sum of thephotocurrent in each detector, so the mean-square signal photocurrentbecomes:<I_(s) ²>8ρP_(r)P_(s).  (15)From the definition of SNR and from equations (12) and (14), SNR for asingle-detector interferometer can be written in terms of P_(r), P_(s),and P_(x), which can be specified for a given interferometerconfiguration:

$\begin{matrix}{{SNR}_{sd} = {\frac{2\rho^{2}P_{r}P_{s}}{\sigma_{re}^{2} + {2q\;{\rho\left( {P_{r} + P_{x}} \right)}B} + {({RIN}){\rho^{2}\left( {P_{r} + P_{x}} \right)}^{2}B}}.}} & (16)\end{matrix}$Similarly, from equations (13) and (15), the expression for SNR for abalanced-receiver interferometer configuration can be written:

$\begin{matrix}{{SNR}_{bd} = {\frac{4\rho^{2}P_{r}P_{s}}{\sigma_{re}^{2} + {2q\;{\rho\left( {P_{r} + P_{x}} \right)}B} + {2\left( {1 + V^{2}} \right)\rho^{2}P_{r}P_{x}{B/\Delta}\; v}}.}} & (17)\end{matrix}$For each interferometer configuration to be discussed, expressions forP_(r), P_(s), and P_(x) will be specified, and σ_(re) ² (which isindependent of source power or interferometer topology) should becalculated as described above. These expressions will also include thecirculator insertion loss as a transmission factor T_(c).As described earlier, the typical OCT configuration is a standardMichelson interferometer (FIG. 1 a). In this case, P_(r)=P₀R_(r)/4,P_(s)=P₀R_(s)/4, and P_(x)=P₀R_(x)4, where P₀ is the power output of theoptical source, and R_(r), R_(s), and R_(x) are the power reflectivitiesof the reference ODL, coherent backscattering from the sample, and theincoherent scattering from the sample arm optics, respectively. Fromequation (16), this results in:

$\begin{matrix}{{SNR} = \frac{\rho^{2}P_{0}^{2}R_{r}{R_{s}/8}}{\begin{matrix}{\sigma_{re}^{2} + {q\;\rho\;{P_{0}\left( {R_{r} + R_{x}} \right)}{B/2}} +} \\{({RIN})\rho^{2}{P_{0}^{2}\left( {R_{r} + R_{x}} \right)}^{2}{B/16}}\end{matrix}}} & (18)\end{matrix}$From inspection of the expressions, it can be seen that receiver noisepower is constant, shot noise power is approximately proportional toR_(r), and excess intensity noise power is approximately proportional toR_(r) ², while <I_(s) ²> is proportional to R_(r). From this, we expectexcess photon noise to dominate for high R_(r), and receiver noise todominate for very low R_(r). It is clear that low reference armreflectivity is required to optimize the standard OCT interferometer,i.e. the reference arm must be attenuated. Again, because it isdesirable to use all available optical source power for imaging, thisconfiguration is not optimum.

For the first embodiment, illustrated in FIG. 6, expressions will bederived for the case of a balanced second coupler and balanceddifferential detection, and for the case of an unbalanced second couple,and a single detector. In the balanced case, for each detector,P_(r)=P₀R_(r)αT_(c) ²/2, P_(s)=P₀R_(s)(1−α)T_(c) ²/2, andP_(x)=P₀R_(x)(1−α)T_(c) ²/2, where α is the splitting ratio of theunbalanced coupler, and T_(c) is the transmission through the circulator(for 0.7 dB insertion loss, T_(c)=0.85). More exact expressions wouldinclude losses due to optical elements, splices, etc. From equation(17), these expressions result in:

$\begin{matrix}{{SNR} = \frac{\rho^{2}P_{0}^{2}{\alpha\left( {1 - \alpha} \right)}R_{r}R_{s}T_{c}^{4}}{\begin{matrix}{\sigma_{\;{re}}^{\; 2} + {q\;\rho\; P_{\; 0}{T_{\; c}^{\; 2}\left( {{R_{r}\alpha} + {R_{x}\left( {1 - \alpha} \right)}} \right)}B} +} \\{\left( {1 + V^{2}} \right)\rho^{2}P_{0}^{2}{\alpha\left( {1 - \alpha} \right)}R_{r}R_{x}T_{c}^{4}{B/2}\Delta\; v}\end{matrix}\;}} & (19)\end{matrix}$The optimization procedure consists of maximizing this expression forSNR as a function of splitting ratio α. The optimum splitting ratiodepends on the properties of the optical source, photodetectors, anddelay line. An explicit expression for the optimum splitting ratio couldby obtained analytically by maximizing the SNR, or alternatively, themodeled SNR could be plotted and the optimum splitting ratio can simplybe read from the plot. The embodiment illustrated in FIG. 6 can also beimplemented with an unbalanced second coupler and a single detector. Inthis case, P_(r)=P₀R_(r)α₁α₂T_(c) ², P_(s)=P₀P_(s)(1−α₁) (1−α₂)T_(c) ²,and P_(x)=P₀R_(x)(1−α₁) (1−α₂)T_(c) ², where α₁ is the splitting ratioof the first coupler and α₂ is the splitting ratio of the secondcoupler. From equation (16), the SNR of this configuration as a functionof splitting ratio is given by:

$\begin{matrix}{{SNR} = \frac{2\rho^{2}P_{0}^{2}R_{r}R_{s}\alpha_{1}{\alpha_{2}\left( {1 - \alpha_{1}} \right)}\left( {1 - \alpha_{2}} \right)T_{c}^{4}}{\begin{matrix}{\sigma_{re}^{2} + {2q\;\rho\; P_{0}{T_{c}^{2}\left( {{R_{r}\alpha_{1}\alpha_{2}} + {{R_{x}\left( {1 - \alpha_{1}} \right)}\left( {1 - \alpha_{2}} \right)}} \right)}B} +} \\{({RIN})\rho^{2}P_{0}^{2}{T_{c}^{4}\left( {{R_{r}\alpha_{1}\alpha_{2}} + {{R_{x}\left( {1 - \alpha_{1}} \right)}\left( {1 - \alpha_{2}} \right)}} \right)}^{2}B}\end{matrix}}} & (20)\end{matrix}$The embodiment illustrated in FIG. 7 is similar to the embodimentillustrated in FIG. 6, except that a transmissive delay line is used inthe reference arm. Consequently, there is no need of a circulator, andno circulator insertion loss associated with the P_(r) expression. Inthe balanced detection case, P_(r)=P₀T_(r)α/2, P_(s)=P₀R_(s)(1−α)T_(c)²/2, and P_(x)=P₀R _(x)(1−α)T_(c) ²/2, where T_(r) is the transmissionthrough the reference delay line. From equation (17), these expressionsresult in:

$\begin{matrix}{{SNR} = \frac{\rho^{2}P_{0}^{2}{\alpha\left( {1 - \alpha} \right)}T_{r}R_{s}T_{c}^{2}}{\begin{matrix}{\sigma_{re}^{2} + {q\;\rho\; P_{0}{T_{c}\left( {{T_{r}\alpha} + {R_{x}\left( {1 - \alpha} \right)}} \right)}B} +} \\{\left( {1 + V^{2}} \right)\rho^{2}P_{0}^{2}{\alpha\left( {1 - \alpha} \right)}T_{r}R_{x}T_{c}^{2}{B/2}\Delta\; v}\end{matrix}}} & (21)\end{matrix}$The embodiment illustrated in FIG. 7 can also be implemented with anunbalanced second coupler and a single detector. In this case,P_(r)=P₀T_(r)α₁α₂, P_(s)=P₀P_(s)(1−₁) (1−α₂)T_(c) ², andP_(x)=P₀R_(x)(1−α₁) (1−α₂)T_(c) ², where α₁ is the splitting ratio ofthe first coupler and α₂ is the splitting ratio of the second coupler.From equation (16), the SNR of this configuration as a function ofsplitting ratio is given by:

$\begin{matrix}{{SNR} = \frac{2\rho^{2}P_{0}^{2}T_{r}R_{s}\alpha_{1}{\alpha_{2}\left( {1 - \alpha_{1}} \right)}\left( {1 - \alpha_{2}} \right)T_{c}^{2}}{\begin{matrix}{\sigma_{re}^{2} + {2q\;\rho\; P_{0}{T_{c}\left( {{T_{r}\alpha_{1}\alpha_{2}} + {{R_{x}\left( {1 - \alpha_{1}} \right)}\left( {1 - \alpha_{2}} \right)}} \right)}B} +} \\{({RIN})\rho^{2}P_{0}^{2}{T_{c}^{2}\left( {{T_{r}\alpha_{1}\alpha_{2}} + {{R_{x}\left( {1 - \alpha_{1}} \right)}\left( {1 - \alpha_{2}} \right)}} \right)}^{2}B}\end{matrix}}} & (22)\end{matrix}$In the embodiment illustrated in FIG. 8, a retroreflecting ODL is usedwithout the need for a second optical circulator. In the balancedreceiver case, for each detector, P_(r)=P₀R_(r)α(1−α)/2,P_(s)=P₀R_(s)(1−α)T_(c) ²/2, and P_(x)=P₀R_(x)(1−α)T_(c) ²/2. Fromequation (17), these expressions result in:

$\begin{matrix}{{SNR} = \frac{\rho^{2}P_{0}^{2}{\alpha\left( {1 - \alpha} \right)}^{2}R_{r}R_{s}T_{c}^{2}}{\begin{matrix}{\sigma_{re}^{2} + {q\;\rho\;{P_{0}\left( {1 - \alpha} \right)}\left( {{R_{r}\alpha} + {R_{x}T_{c}^{2}}} \right)B} +} \\{\left( {1 + V^{2}} \right)\rho^{2}P_{0}^{2}{\alpha\left( {1 - \alpha} \right)}^{2}R_{r}R_{x}T_{c}^{2}{B/2}\Delta\; v}\end{matrix}}} & (23)\end{matrix}$The embodiment illustrated in FIG. 8 can also be implemented with anunbalanced second coupler and a single detector. In this case,P_(r)=P₀R_(r)α₁α₂ (1−α₁), P_(s)=P₀R_(s)(1−α₁) (1−α₂)T_(c) ², andP_(x)=P₀R_(x)(1−₁) (1−α₂)T_(c) ². From equation (16), the SNR of thisconfiguration as a function of splitting ratio is given by:

$\begin{matrix}{{SNR} = \frac{2\rho^{2}P_{0}^{2}R_{r}R_{s}\alpha_{1}{\alpha_{2}\left( {1 - \alpha_{1}} \right)}^{2}\left( {1 - \alpha_{2}} \right)T_{c}^{2}}{\begin{matrix}{\sigma_{re}^{2} + {2q\;\rho\;{P_{0}\left( {1 - \alpha_{1}} \right)}\left( {{R_{r}\alpha_{1}\alpha_{2}} + {{R_{x}\left( {1 - \alpha_{2}} \right)}T_{c}^{2}}} \right)B} +} \\{({RIN})\rho^{2}{P_{0}^{2}\left( {1 - \alpha_{1}} \right)}^{2}\left( {{R_{r}\alpha_{1}\alpha_{2}} + {{R_{x}\left( {1 - \alpha_{2}} \right)}T_{c}^{2}}} \right)^{2}B}\end{matrix}}} & (24)\end{matrix}$The embodiment illustrated in FIG. 9 uses a Michelson interferometerefficiently by introducing an optical circulator into the source arminstead of the sample arm, as in the previous embodiments. Thisembodiment uses an unbalanced splitter and a single detector. Here,P_(r)=P₀R,α², P_(s)=P₀P_(s)(1−α)²T_(c) ², and P_(x)=P₀P_(x)(1−α)²T_(c)², and from equation (16), the SNR of this configuration as a functionof splitting ratio is given by:

$\begin{matrix}{{SNR} = {\frac{2\rho^{2}P_{0}^{2}R_{r}R_{s}{\alpha^{2}\left( {1 - \alpha_{1}} \right)}^{2}T_{c}^{4}}{\begin{matrix}{\sigma_{re}^{2} + {2q\;\rho\; P_{0}{T_{c}^{2}\left( {{R_{r}\alpha^{2}} + {R_{x}\left( {1 - \alpha_{1}} \right)}^{2}} \right)}B} +} \\{({RIN})\rho^{2}P_{0}^{2}{T_{c}^{4}\left( {{R_{r}\alpha^{2}} + {R_{x}\left( {1 - \alpha_{1}} \right)}^{2}} \right)}^{2}B}\end{matrix}}.}} & (25)\end{matrix}$The embodiment illustrated in FIG. 10 utilizes a balanced receiver.Here, for each detector, P_(r)=P₀R_(r)T_(c) ²/4, P_(s)=P₀R_(s)T_(c) ²/4,and P_(x)=P₀R_(s)T_(c) ²/4, assuming detector d2 is attenuated by anamount equivalent to T_(c). From equation (17), these expressions resultin:

$\begin{matrix}{{SNR} = {\frac{\rho^{2}P_{0}^{2}R_{r}R_{s}{T_{c}^{4}/4}}{\begin{matrix}{\sigma_{re}^{2} + {q\;\rho\; P_{0}{T_{c}^{2}\left( {R_{r} + R_{x}} \right)}{B/2}} +} \\{\left( {1 + V^{2}} \right)\rho^{2}P_{0}^{2}T_{c}^{4}R_{r}R_{x}{B/8}\;\Delta\; v}\end{matrix}}.}} & (26)\end{matrix}$It must be noted that this embodiment uses a single balanced coupler andtherefore there is no optimization required beyond balancing thedetectors. This embodiment has the significant advantage that anexisting fiber-optic Michelson interferometer OCT system can be easilyretrofitted with a circulator in the source arm and a balanced receiverwith no need to disturb the rest of the system. We have recentlydemonstrated this embodiment in a high-speed endoscopic OCT system.

There are many practical applications for using OCDR and OCT to imagetransmissive samples, rather than reflective samples. Here we definetransmissive as any sample illumination and collection geometry in whichthe illumination and collection optics occupy separate optical paths,for example using separate fibers for illumination and collection oflight from the sample. The path of light through the sample may be in astraight line, in which case the illumination and collection opticswould be lined up along a path aimed directly through the sample.Alternatively, the path of light through the sample may be transmissivein the sense illustrated in FIGS. 11-13, in which there is some angle(other than 0 or 180 degrees) between the illumination and collectionoptical directions. Although these latter configurations are in somesense reflective geometries, for the purposes of this description wedefine them as transmissive so long as separate optical paths are usedfor illumination and collection. In the straight-line geometry (with anangle of 180 degrees between the illumination and collection optics),OCDR and OCT can be used to form images of the internal structure ofbiological or other materials. In the non-straight line geometry (withany angle other than 0 or 180 degrees between the illumination andcollection optics), OCDR and OCT may be used to probe the internalstructure of biological or other materials in cases in which it is notconvenient to use a retro-reflection geometry (as in embodiments 1-5).There may be other compelling reasons to use an off-axisillumination/collection geometry, for example such geometries may beespecially sensitive to internal features of the structure of the sample(e.g., cell nucleus sizing in biological tissues).

We disclose three further embodiments (embodiments 6 through 8,illustrated in FIGS. 11-13, respectively) which are similar in manyrespects to embodiments 1 through 3, respectively, except that they aredesigned to accommodate samples which are transmissive rather thanreflective.

Embodiment 6

This embodiment is similar in all respects to embodiment 1, except thata transmissive sample is used in the place of the circulator and samplein embodiment 1.

Under the assumption of shot-noise limited detection, the expressionsfor SNR of this embodiment using dual-balanced and single-detectorconfigurations are given by equations (3) and (5), respectively, underthe conditions that T_(c)=1 (since there is no circulator in embodiment6) and that R_(s) is interpreted as the transmission of the samplerather than its reflectivity. The optimal splitting ratios for the firstunbalanced coupler and for both unbalanced couplers using dual-balancedand single-detector configurations are given by equations (4) and (6),respectively, under these same conditions.

Under the assumption that the more sophisticated signal-to-noise ratioanalysis must be used, the expressions for SNR of this embodiment usingdual-balanced and single-detector configurations are given by equations(19) and (20), respectively, again under the conditions that T_(c)=1(since there is no circulator in embodiment 6) and that R_(s) isinterpreted as the transmission of the sample rather than itsreflectivity. The procedures for optimizing the splitting ratios for thefirst unbalanced coupler and for both unbalanced couplers usingdual-balanced and single-detector configurations are the same asdescribed for the reflective sample configurations immediately followingequations (19) and (20), respectively.

Embodiment 7

This embodiment is similar in all respects to embodiment 2, except thata transmissive sample is used in the place of the circulator and samplein embodiment 1.

Under the assumption of shot-noise limited detection, the expressionsfor SNR of this embodiment using dual-balanced and single-detectorconfigurations are also given by equations (3) and (5), respectively,under the conditions that T_(c)=1 (since there is no circulator inembodiment 7) and that R_(s) is interpreted as the transmission of thesample rather than its reflectivity. The optimal splitting ratios forthe first unbalanced coupler and for both unbalanced couplers usingdual-balanced and single-detector configurations are given by equations(7) and (8), respectively, under these same conditions.

Under the assumption that the more sophisticated signal-to-noise ratioanalysis must be used, the expressions for SNR of this embodiment usingdual-balanced and single-detector configurations are given by equations(21) and (22), respectively, again under the conditions that T_(c)=1(since there is no circulator in embodiment 7) and that R_(s) isinterpreted as the transmission of the sample rather than itsreflectivity. The procedures for optimizing the splitting ratios for thefirst unbalanced coupler and for both unbalanced couplers usingdual-balanced and single-detector configurations are the same asdescribed for the reflective sample configurations immediately followingequations (21) and (22), respectively.

Embodiment 8

This embodiment is similar in all respects to embodiment 3, except thata transmissive sample is used in the place of the circulator and samplein embodiment 3.

Under the assumption of shot-noise limited detection, the expressionsfor SNR of this embodiment using dual-balanced and single-detectorconfigurations are also given by equations (3) and (5), respectively,under the conditions that T_(c)=1 (since there is no circulator inembodiment 8) and that R_(s) is interpreted as the transmission of thesample rather than its reflectivity. The optimal splitting ratios forthe first unbalanced coupler and for both unbalanced couplers usingdual-balanced and single-detector configurations are given by equations(7) (under the assumption that α₁ is small) and (8) (under theassumption that both α₁ and α₂ are small), respectively, under thesesame conditions.

Under the assumption that the more sophisticated signal-to-noise ratioanalysis must be used, the expressions for SNR of this embodiment usingdual-balanced and single-detector configurations are given by equations(23) and (24), respectively, again under the conditions that T_(c)=1(since there is no circulator in embodiment 8) and that R_(s) isinterpreted as the transmission of the sample rather than itsreflectivity. The procedures for optimizing the splitting ratios for thefirst unbalanced coupler and for both unbalanced couplers usingdual-balanced and single-detector configurations are the same asdescribed for the reflective sample configurations immediately followingequations (23) and (24), respectively.

Although various embodiments and aspects of the invention have beendescribed herein in detail, it is recognized that modifications,improvements, and variations can be made without departing from thespirit and scope of the invention as set forth in the accompanyingclaims.

1. An interferometer for use in an OCDR or OCT imaging system to image asample, comprising: an optical radiation source; a nonreciprocal opticalelement having a first input connected to receive optical radiation fromthe optical radiation source and a combination first output/secondinput; and a beamsplitter having a first input connected to thecombination first output/second input of the nonreciprocal opticalelement, the beamsplitter having a first output connected for directingoptical radiation to a sample to be imaged and for receiving reflectedoptical radiation from the sample to be imaged, and the beamsplitterhaving a second output connected for directing optical radiation to areference delay element and for receiving reflected optical radiationfrom the reference delay element.
 2. Interferometer of claim 1, furthercomprising: an optical radiation detector connected to receive opticalradiation from a second output of the non reciprocal optical element. 3.The interferometer of claim 2, wherein the optical radiation detectorcomprises a first optical radiation detector connected to receiveoptical radiation from a second output of the non reciprocal opticalelement and a second optical radiation detector connected to receiveoptical radiation from a second input of the beamsplitter. 4.interferometer of claim 3, wherein the first optical radiation detectorand the second optical radiation detector are connected to form adifferential optical radiation detector.
 5. The interferometer of claim3, wherein the first optical radiation detector and the second opticalradiation detector are connected to form a differential detector.
 6. Theinterferometer of claim 1, wherein the beamsplitter comprises a balancedbeamsplitter.
 7. The interferometer of claim 1, wherein the beamsplittercomprises an unbalanced beamsplitter.
 8. The interferometer of claim 1,wherein the beamsplitter is an unbalanced beamsplitter that delivers atleast 85% of the optical radiation received at the first input to thefirst output.
 9. The interferometer of claim 1, wherein thenonreciprocal optical element comprises an optical circulator.
 10. Theinterferometer of claim 1, further comprising a beamsplitter connectedbetween the optical radiation source and the nonreciprocal opticalelement.
 11. The interferometer of claim 1, further comprising one ormore beamsplitters connected between the optical radiation source andthe nonreciprocal optical element.
 12. An interferometer system forimaging a sample at a sample location, comprising: an optical radiationsource, a beamsplitter, and an optical circulator connected between theoptical radiation source and the beamsplitter for transmitting opticalradiation from the optical radiation source through the opticalcirculator to a sample location, an output of the optical circulatorbeing connected to direct optical radiation to an optical radiationdetector.
 13. The interferometer of claim 12, wherein the opticalcirculator comprises a Faraday rotator and a polarizing beamsplitter.14. The interferometer of claim 12, wherein the beamsplitter includes afirst output connected to direct light to the sample location and asecond output connected to direct light to a reference location.
 15. Theinterferometer of claim 12, further comprising a beamsplitter connectedbetween the optical radiation source and the nonreciprocal opticalelement.
 16. The interferometer of claim 12, wherein the opticaldetector comprises first and second optical detectors, the first opticaldetector connected to the optical circulator and the second opticaldetector coupled to the beamsplitter.
 17. An interferometer system forimaging a sample at a sample location, the interferometer comprising: anoptical radiation source, a nonreciprocal optical element, abeamsplitter and an optical detector; a first optical path extendingfrom the optical radiation source, through a first portion of thenonreciprocal optical element, through the beamsplitter to a samplelocation, and from the sample location through the beamsplitter and asecond portion of the nonreciprocal optical element to the opticaldetector.
 18. The interferometer of claim 17, wherein the opticaldetector comprises first and second optical detectors, the first opticaldetector positioned at the end of the first optical path, theinterferometer further comprising: a second optical path extending fromthe optical radiation source, through the first portion of thenonreciprocal optical element and through the beamsplitter to areference location, and from the reference location to the secondoptical detector.
 19. The interferometer of claim 17, furthercomprising: a second optical path extending from the optical radiationsource, through the first portion of the nonreciprocal optical elementto a reference location, from the reference location through the secondportion of the nonreciprocal optical element to the optical detector.20. The interferometer of claim 17, wherein the nonreciprocal opticalelement is an optical circulator.